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Investigation of the letter, allegedly
written by Leibnizby Leonhard Euler,
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Mr. de Maupertuis, President of the Royal Academy, has
shown (by several very convincing arguments) that the action is
always minimized, not only at equilibrium but also in the motions
of bodies under external forces; this remarkable principle of
least action expresses the most general law of Nature.
Professor König, however, has tried in several ways to
destroy this great discovery. First, he does not believe that it
pertains to equilibrium problems, which he suggests corresponds not
to the minimum of the action, but rather to where the
action is zero; to support his case, he gives several
examples in which minimization of the action results in zero
action. However, this criticism is irrelevant, since it is
recognized in the calculus of minima and maxima that a minimized
quantity disappears entirely. Although König's "zero action
principle" may apply in certain cases, it cannot be extended to all
cases; for there are an infinite number of cases in which the
action is minimized, but not zero. Hence, beyond any doubt,
Nature's goal is to minimize the action, rather than set
it to zero. If we consider the example of the "chain curve" (the
catenary), where the total action is defined as the distance of the
center of gravity of the chain to the center of the Earth, clearly
this distance cannot be zero; rather, and most effectively, it
should adopt the smallest possible value. It is indeed true that
the force of gravity, given no resistance, would pull the chain to
the center of the Earth, and that the only equilibrium position of
the chain in that case would be at the center of the earth.
However, since the chain is impeded at its points of suspension,
the effect of gravity is limited to making the distance between the
centers of gravity of the chain and the Earth as small as possible.
Of course we agree with Mr. König that the action is
indeed zero in those cases where it is true; however, this is not
always possible, as we may see from the brachistochrone problem;
rather, the action is to be minimized. It is as though Nature
wishes to achieve some effect, and approaches it as closely as
possible. Not only is the truth of this principle evidence, but
also the reasoning upon which it is based, and to destroy entirely
the objections of Mr. König who, far from striking a blow
against this principle, has wonderfully helped to confirm it. It is
a specious criticism of the principle of least action to note that
there are certain cases in which the action disappears entirely,
since the action can assuredly not become smaller than zero.
Nevertheless, this objection might have some merit, if the action
were reduced to zero in every case of equilibrium, as Mr.
König seems to insinuate; but that cannot be proven, since
there is an infinite number of cases in which the action is clearly
not zero, but rather adopts the smallest possible value. In
addition to the catenary problem, Mr. D. Bernoulli and Mr.
Euler have shown that the elastic curves of every type and
other figures adopted by flexible bodies (when the forces acting on
them are in equilibrium) may be found by a method of maxima and
minima applied to a formula that always contains the action, which
is to be minimized and not set to zero.

Mr. König also criticized Maupertuis' excellent principle
of least action for motion and, although he did not attack its
validity, his remarks require serious attention. Being unable to
shake the foundations of this principle, König now seeks to rob Mr.
de Maupertuis of the glory of its invention and give it to
Mr. Leibniz. For this purpose, he quotes from a letter
allegedly written by Mr. Leibniz to Mr. Hermann,
as follows

The action is not at all what you imagine, since time is
involved. The action is rather the product of the mass and the
time, or the time multiplied by the kinetic energy. I have noticed
that, in changes of motion, the action is either minimized or
maximimized. One can derive from that several important results,
such as the paths followed by bodies attracted to one or several
centers of force. I would like to address these topics (among
others) in the second part of my Dyanmics, which I have
suppressed, due to the biased reception of the first
part.

It follows from this passage that Mr. Leibniz not only
knew the sublime principal of least action, but also was able to
derive the paths of bodies attracted by one or several centers of
force. This raised the first suspicions about this passage, all the
more since the letter itself (from which this quote was taken) has
never been published. Therefore, it became necessary to determine
whether this letter was indeed written by Mr. Leibniz, by
identifying the place where the original existed; otherwise, such
evidence is worthless, especially in a case like this one, which
concerns a discovery of such importance. For these reasns, it
became utterly necessary to prove the authenticity of the
quotation. First, the published letters of Mr. Leibniz
were carefully reviewed, letters in which his sublime thoughts on
every type of science can be appreciated and admired; however, Mr.
Leibniz did not reveal this admirable principle of least
action to any other friend. In particular, Leibniz had a long and
intimate friendship with the renowned Mr. Johann
Bernoulli, with whom he often conversed about dynamics;
although their long correspondence contains several discussions of
kinetic energy and the correct way of calculating the action, it
does not contain any indication that Mr. Leibniz ever
thought of the principle of least action. Considering that Mr.
Leibniz hid nothing from Mr. Bernoulli anything
that could support his theory of kinetic energy or extend its
application, one cannot imagine any reason to keep this least
action principle secret.

Moreover, concerning the determination of paths followed by bodies
attracted to one or several centers of force, the method of maxima
and minima necessary to determine these paths had not been
sufficiently developed to carry out that calculation, even if it
had been known that the action ought to be minimized. And although
the glory of Mr. Leibniz rests on several discoveries of
the first rank, the principle of least action would be equal to
them all; it cannot be believed that he would impart this discovery
to no one except Mr. Hermann.

Since these considerations had already weakened the credibility of
this quotation, President de Maupertuis (who proposed the
principle of least action as his own invention) felt it necessary
to search for proof of his priority, to protect himself from every
suspicion of plagiarism. Although there is no trace of the least
action principle in the published writings of Mr. Leibniz,
one must hinder the potential accusation that he had taken his
principle from the same letter of Mr. Leibniz, which
perchance might have come into his hands. Since no one is more
concerned with the credibility of the letter than Mr. de
Maupertuis, he began to write to Mr. König himself,
asking him (in a friendly letter dated 28 May 1751) to show the
original of the letter and establish its authenticity. Mr.
König did not reply until June 26th. He claimed that the
letter had been communicated to him by the famous Henzi,
who was decapitated in Berne three years ago for inciting sedition
against the State, and that Henzi, being much attached to the
study, had collected letters attributed to Leibiz and would have
published them, had he not been prevented by fate. At the same
time, M. König sent to Mr. de Maupertuis a copy
of the entire letter that he had quoted, which was dated 16 October
1707. The quotation was found near the end, but with a slight
change of wording; instead of the original wording

The action is rather the product of the mass and the time,
or the time multiplied by the kinetic energy.

which contains a clear contradiction, the letter itself
contained the correct wording

The action is rather the product of the mass, distance and
speed, or the time multiplied by the kinetic energy.

This difference in wording, which could not have been a simple
printer's error, increased considerably the suspicions surrounding
this fragment. Although the entire letter could not be rejected, it
seemed plausible that certain phrases and even entire sentences had
been introduced, and that one did not make them match sufficiently
with the remaining text. On top of this suspicion, it seemed
regrettable that the credibility of this fragment depended entirely
on the testimony of a man who had lost his head; and that such
testimoney was insufficient to establish its authenticity.
Nevertheless, Mr. de Maupertuis felt that he should not
confine himself to Mr. König's response; and, given that
no one's papers are guarded more carefully than those of an enemy
of the State, he asked the Marquis de Paulmy, Ambassador
of SMTC in Switzerland, to use his influence to have the papers
left behind by Henzi in Berne investigated. A careful
investigation showed not only that Mr. Henzi had no
letters of Leibniz, but not even the smallest sign that he had ever
had even one such letter in his possession.

On October 7th of last year (1751), President de
Maupertuis reported to the Royal Academy everything that had
occurred up to that point, with the intention that the affair be
handled according to the proper forms, and that it be ended with
suitable measures. The Academy judged immediately that, in a
question that concerns such an important discovery, one ought to
conduct a careful examination of what pertains to the great
Leibniz and to what its members have a right. The Academy
charged Mr. Formey, in his post as Secretary, to write to
Mr. König a letter (which was written the following day)
to request again in a friendly way that he confirm the authenticity
of the fragment he had alleged, and to produce the original letter
of Leibniz within a month. However, Mr. König had
used delaying tactics in this affair, and to prevent him from
claiming that the Academy's letter had been lost, the Academy also
sent a copy of its letter to Mr. de Hellen, the chargé
des affaires of his Majesty for the General States, who
testified that the letter was delivered on the 19th of October. On
the 11th of December, at which point over a month had passed
without any response, the Academy decided to reiterate its request.
One is certain that Mr. König received that second letter,
along with a letter written by the President, who delivered it
himself on the 6th of January of this year (1752).

During this time, the King himself, the Protector of the Academy,
sent a letter to the Magistrate in Berne, requesting him to search
for the letter (reputedly) of Leibniz among all possible
papers of Henzi. This search was carried out by assistants
to the Magistrate himself, with the result that absolutely nothing
was found.

Before the second letter of the Academy to Mr. König had
arrived, Mr. de Maupertuis himself received a letter dated
the 10th of December, which he read to the Academy on the 23rd of
the same month. Although the ;etter was full of politeness,
Mr. König seemed far off from producing the original
letter of Mr. Leibniz, or even to state the place where it
existed. Instead he tried to divert the attention of the Academy
from this question, and to implicate other controversies foreign to
the question at hand. He complained a lot about the injustice to
which he was being subjected, expecting the freedom that scholars
enjoy by custom, as though it were a injust to demand of a scholar
that he provide proof of a letter that he made public.

The same day that Mr. de Maupertuis read his own response
to this letter, in which he defended the right of the Academy to
establish the authenticity of writings that helped to determine who
deserved credit for certain discoveries, and that there was nothing
wrong in demanding of Mr. König that he produce the
original letter of Mr. Leibniz; no other controversy was
involved and nothing else was reuiqred of him except that he
establish the authenticity of the letter he had cited, which should
not be refused by anyone, particularly in their own defence. In the
same letter, Mr. de Maupertuis reported to Mr.
König the two searches that had been carried out in vain
in Berne, as ordered by the King and by the Ambassador of France.
This reply was endorsed unanimously by the Academy was delivered on
the 6th of January of this year (1752), along with the second
letter of the Academy to Mr. König.

The reply to these letters was dated the 15th of February. In this
letter, as in its predecessor, Mr. König complained
bitterly about what he regarded as a violation of his rights as a
scholar of letters with the involvement of the Academy's authority
in a controversy of literature. He continued to dissimulate
concerning the state of the question, and did not respond at all to
the one request made of him, that he confirm the authenticity of
the fragment he had quoted by producing the original letter of Mr.
Leibniz. He looked everywhere for an escape. Sometimes he
would say that the words of Leibniz did not remove
anything from the discovery of the principle of least action, that
Mr. de Maupertuis preserved the right to attribute it to
himself, since the letter was completely unknown up to the present
and that Mr. Leibniz had not revealed or extended his
ideas on the subject. Sometimes he would claim that Mr.
Leibniz was even opposed to this principle, having perhaps
had a different principle in mind, where Mr. König tried
to cast doubt on the principle itself, rather than dealing with the
question at hand, the authenticity of the letter. Yet in the end,
he seemed to be moved to action, saying that he had written to a
friend to ask him to look for the original, and that he was still
expecting his reply.

It should be noted that, in the same letter, Mr. König
appealed to his first publication where, seeking to show that Mr.
Leibniz had known of this discovery for a long time, he
said he had suppressed this discovery. (unclear translation)
Although this assertion would have to be similarly proven, and
would require a certain authority to give it credibility in the
province of letters, it seems implausible that Mr.
Leibniz, tired of the criticism of evil judges, would not
want to publish the second part of his Dynamics, to the
irreparable harm of science, so that the ignorant would not regard
his principles as monstrous chimeras. However, one sees well enough
that this suppression has little to do with the present affair,
which is restricted to demanding of Mr. König that he
justify his quotation by producing the original letter.

At the same time, additional searches were carried out in Basel,
where Mr. Hermann died, to dig up the letters which he had
received from Mr. Leibniz. The results of these searches
showed clearly that such letters had long been in the hands of Mr.
König, and that it would be useless work to look for them
in other places. No others have been found, and there is not yet
any reason to suspect that some have been lost.

The Magistrate in Basel was required by the King to examine in
detail all the papers left behind by Mr. Hermann and
preserved by his heirs. Mr. Johann Bernoulli, Professor of
Mathematics, who was charged with this commission, found only three
letters of Mr. Leibniz, which contained no mention of the
principle of least action.

In a letter dated the 12th of March, Mr. König said that
he had searched in vain, with the help of a friend, for this letter
of Leibniz among the papers left behind by Mr.
Hermann and he sent at the same time the reply he had
received on the subject. He added that the attention he was giving
to this reply was the reason causing him to treat the main question
only lightly, but that he believed that his demonstrated diligence
in searching for the original letter ought to satisfy the
Academy.

These matters are such that they may be reported. The quotation is
intrinsicially suspicious; and Mr. König, after learning
that the original letter of Mr. Leibniz could not be found
in the papers of Henzi (to whom he had referred), has not
produced the original, nor has he been able to identify the place
where it is preserved. Hence, it is assuredly obvious that his
cause is bad, and that this quotation is a forgery, either to put
Mr. de Maupertuis in the wrong, or to exaggerate (as if by
pious fraud) the praises of the great Leibniz, who without
question does not need such help. Having weighed these
considerations appropriately, the Academy does not hestitate to
declare this quotation fraudulent and to strip it of any
credibility it might have ever possessed.

Curator de Keith remitted to the Academy the following
letter from President de Maupertuis, which the Secretary
read.

Sir,

Since the Academy has heard today the summary of Mr. Euler
on the subject of the letter cited by Mr. König and has
pronounced its judgment on the affair, I have the honor of
reporting that I was in no way implicated. Since I do not wish any
reparations from Mr. König, I ask the Academy only to
continue to ask for verification, i.e., evidence for the
authenticity of the letter of Mr. Leibniz that Mr.
König cited. I have the honor of being, etc.

Maupertuis

The Secretary assembled for the Bureau all the documents
pertaining to the affair between Mr. König and the
Academy, gave a summary and read in their entirety certain
documents that had never been communicated to the Academy (such as
the letter from Mr. König to Mr. Formey of 15
February 1752, a letter of Mr. de Maupertuis to Mr.
König of 9 February 1752 and the reply of Mr.
König to that letter of 12 March 1752), to which he
attached the latest evidence concerning the letters of Mr.
Leibniz, sent to SM by MM the Magistrates of Basel.

Director Euler then read a report in Latin, where he
alleged that all the evidence (both concrete and that arrived at by
reasoning) showed that the passage alleged by Mr. König to
have been quoted from a letter of Mr. Leibniz was
suspicious on its own and clearly false given the
circumstances.

Upon this point, Curator de Keith polled all the present
members of the Academy, with the following unanimous result:

that the passage published by Mr. König in
the Acta Eruditorum of Leipzig as a quotation from a
letter of Mr. Leibniz written in French to Mr.
Hermann, appears to be a forgery and, consequently, does not
carry even a shadow of authority concerning the legitimate rights
of the Academy members involved in this affair, to take credit for
the principles developed from their meditations and research (and
for everything that may be derived from them) in reports adopted by
the Academy and in its other publications; and that the conclusions
drawn by Mr. Euler in his report are just and worthy, with
all the force of the terms in which they were expressed. After
considering the letter of Mr. de Maupertuis read at the
beginning of the meeting, the Academy does not wish to press the
matter further and concludes its deliberations concerning Mr.
König, as it is authorized to do for such
proceedings.

Keith.Redern.Eller.Heinius.Euler.Formey Secr. perp.

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